Finite Group DatabasebetaFinite Group Databasebeta| order | 7456 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C233 ⋊ #126 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D233 |
| commutator, socle | C22×C233 | C23 |
| Fitting | C22⋊C4×C233 | C2 |
| hypercenter | C22⋊C4 | D233 |
| hypocenter | C233 | #126 |
| LCS | G ▷ C22×C233 ▷ C233 | |
| UCS | C1 ◁ C22 ◁ C22⋊C4 | |
60 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,233|b^2=de,c^2=d,b^a=bd,c^a=ce,f^c=f^2321174 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #126×D233, C2×#21418528, #28416962, … |
| maximal normal subgroup of | #126×D233, C2×#21418528, #28416962, … |
| maximal quotient of | #28416302, #28416317, #28416320, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7456, 139);